Friday, 05 November 2010

In Passing

Mark Twain on mathematical extrapolation


Roberta has put up a post in which she marvels at

...how short a time it took for statistical analysis of mass behavior of large groups to be considered with an eye to predicting and possibly manipulating the outcome.
Her citations of a couple of pre-World-War-II projects give me an excuse for hauling out this 1883-vintage example of mathematical prediction which still should stand as a lesson to us all.

(As Mr.Clemens spends a couple of pages setting things up, you’ll find it all  below the break.)

from Life on the Mississippi:
Chapter 17: Cut-offs and Stephen

THESE dry details [steamboat speed records] are of importance in one particular.  They give me an opportunity of introducing one of the Mississippi’s oddest peculiarities– that of shortening its length from time to time.  If you will throw a long, pliant apple-paring over your shoulder, it will pretty fairly shape itself into an average section of the Mississippi River; that is, the nine or ten hundred miles stretching from Cairo, Illinois, southward to New Orleans, the same being wonderfully crooked, with a brief straight bit here and there at wide intervals...

The water cuts the alluvial banks of the lower river into deep horseshoe curves; so deep, indeed, that in some places if you were to get ashore at one extremity of the horseshoe and walk across the neck, half or three quarters of a mile, you could sit down and rest a couple of hours while your steamer was coming around the long elbow, at a speed of ten miles an hour, to take you aboard again.  When the river is rising fast, some scoundrel whose plantation is back in the country, and therefore of inferior value, has only to watch his chance, cut a little gutter across the narrow neck of land some dark night, and turn the water into it, and in a wonderfully short time a miracle has happened: To wit, the whole Mississippi has taken possession of that little ditch, and placed the countryman’s plantation on its bank (quadrupling its value), and the other party’s formerly valuable plantation finds itself away out yonder on a big island...  Watches are kept on these narrow necks at needful times, and if a man happens to be caught cutting a ditch across them, the chances are all against his ever having another opportunity to cut a ditch.

Pray observe some of the effects of this ditching business.  Once there was a neck opposite Port Hudson, Louisiana which was only half a mile across, in its narrowest place.  You could walk across there in fifteen minutes; but if you made the journey around the cape on a raft, you traveled thirty-five miles to accomplish the same thing. In 1722 the river darted through that neck, ...and thus shortened itself twenty-five miles.  In the same way it shortened itself twenty-five miles at Black Hawk Point in 1699.  Below Red River Landing, Raccourci cutoff was made (forty or fifty years ago, I think).  This shortened the river twenty-eight miles.  In our day, if you travel the river from the southernmost of these cutoffs to the northernmost, you go only seventy miles.  To do the same thing a hundred and seventy-six years ago, one had to go a hundred and fifty-eight miles!-- shortening of eighty-eight miles in that trifling distance...

Since my own day on the Mississippi, cut-offs have been made at Hurricane Island; at island 100; at Napoleon, Arkansas; at Walnut Bend; and at Council Bend.  These shortened the river, in the aggregate, sixty-seven miles...

...The Mississippi between Cairo and New Orleans was twelve hundred and fifteen miles long one hundred and seventy-six years ago.  It was eleven hundred and eighty after the cut-off of 1722.  It was one thousand and forty after the American Bend cut-off. It has lost sixty-seven miles since.  Consequently its length is only nine hundred and seventy-three miles at present.

Now, if I wanted to be one of those ponderous scientific people, and ‘let on’ to prove what had occurred in the remote past by what had occurred in a given time in the recent past, or what will occur in the far future by what has occurred in late years, what an opportunity is here! ...  Please observe:--

In the space of one hundred and seventy-six years, the Lower Mississippi has shortened itself two hundred and forty-two miles.  This is an average of a trifle over one mile and a third per year.  Therefore, any calm person, who is not blind or idiotic, can see that in the Old Oolitic Silurian Period, just a million years ago next November, the Lower Mississippi River was upwards of one million three hundred thousand miles long, and stuck out over the Gulf of Mexico like a fishing-rod.  And by the same token any person can see that seven hundred and forty-two years from now the Lower Mississippi will be only a mile and three-quarters long, and Cairo and New Orleans will have joined their streets together, and be plodding comfortably along under a single mayor and a mutual board of aldermen.

There is something fascinating about science.  One gets such wholesale returns of conjecture out of such a trifling investment of fact...

Posted by: Old Grouch in In Passing at 16:51:41 GMT | No Comments | Add Comment
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